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Department of Mathematics
Rand Afrikaans University
PO Box 524
Auckland Park 2006
Johannesburg
South Africa
vfg@na.rau.ac.za
http://www.rau.ac.za/staff/goranko_vf
We study a generic problem of proving semantic completeness of a logical system with respect to a class of ``standard models'', provided a weaker completeness result with respect to a larger class of ``general models'' has been obtained. We propose a natural topological approach to this problem based on the notion of logical topology and the related concept of logical approximation. We then obtain some general results regarding these concepts and then discuss them in the framework of first-order logic. The paper ends with an example of a particualr application of the ideas developed here, and a discussion on further research.